Was Joan estimate within 0.5 hours of the actual time that the trip took off?
Statement 1: Joan’s estimate for the distance was within 5 miles of the actual distance.
$$Time\ taken=\frac{dis\tan ce}{speed}$$
This statement gives the estimate of Joan's distance but nothing regarding the estimate of her speed, hence, statement 1 is NOT SUFFICIENT.

Statement 2: Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.
This statement gives the estimate of her average speed but nothing regarding the estimate of the distance she covered. Therefore, this statement is NOT SUFFICIENT.

Combining both statements together:
There is a possible scenario of perfectly accurate estimates in which Joan's travel time will be equal to her estimated time, and it will be within 0.5 hours.
i.e 5/10 = 1/2 = 0.5
There is another possible scenario in which estimates are NOT ACCURATE.
If estimated, distance and speed are 10 miles and 8 miles per hour and actual distance and speed are 7 miles and 7 miles per hour respectively.
Estimated travel time = 10/8 = 1.25
Actual travel time = 7/7 = 1 hour

The estimated travel time is still within 0.5 hours of actual travel time as 1 -1.25 = 0.25 hours.
But if the estimated distance and speed are 10 miles and 10 miles per hour, and actual distance and speed are 7 miles and 3 miles per hour respective;y, then,
$$Estimated\ time\ taken=\frac{10}{10}=1\ hour$$
$$Actual\ time\ taken=\frac{7}{3}=2.3\ hours$$
The estimated travel time is no longer within 0.5 hours of actual travel time, it is now within 2.3 - 1 = 1.3 hours.
Since the target question cannot be answered with certainty, then, both statements together are NOT SUFFICIENT. Therefore, option E is the correct answer.